Big consumer brands looking to market themselves on Facebook have a fresh problem on their hands: smut.

“I am a girl who has an innocent face but has a big appetite for s-e-x,” said a young woman identified as “Leona O’Brien” on Nike’s Facebook page yesterday, standing out from a cluster of legitimate photos posted by Nike enthusiasts modeling their gear.

“I’ll definitely put a smile in your face after tonight baby,” cooed another on the Levi’s Facebook page, which yesterday was riddled with similarly suggestive fare amid photos of regular customers showing off their jeans.

Raunchy spam was found by The Post on other Facebook pages for big-name brands, including Victoria’s Secret and Aeropostale. In each case, the come-ons included links to sexy hook-up sites with names like xxxblackbook, ihookup and Adult FriendFinder — the X-rated dating site operated by FriendFinder, the owner of Penthouse magazine.

A Facebook spokesman said the company doesn’t comment on “volume of attacks or specific cases” of spamming. “We’re working on ways to automate the flagging of these scams so we can take action on them even more quickly,” according to a statement on Facebook’s site.

But Nike, after receiving a query from The Post yesterday afternoon, appeared to have blocked access to mostly all of the photos on its Facebook page within hours.

“We have been spammed on one of our sites,” a Nike spokesman said. “We extend our apologies and have removed the offensive content.”

A Levi’s spokeswoman, Alexa Rudin, said the denim giant’s policy is “to remove offensive content as soon as possible and to report violations to Facebook.”

Nevertheless, the dirty spam had littered the Levi’s Facebook page for at least a week, according to one source.

“I’ve been online watching these issues for more than a decade, and I’m a bit shocked,” said Chris Cunningham, CEO of appssavvy, a social-media focused marketing firm. “What’s fascinating here is that typically Facebook’s technology and reporting would catch something like this and instantly shut it down.”

But with filth infiltrating Facebook, corporate members should take a lesson.

On social-media sites, “It’s more about understanding your role as a steward, a moderator, a guide for your brand — not as a dictator,” says Ray Graj of Graj + Gustavsen, a New York branding consultant. “Brands think they have this control, but they don’t.”

Nevertheless, “I don’t think the solution is putting your head in the sand and not being on Facebook,” Graj added. “You need to be in it and monitoring it and with it.” –with Claire Atkinson